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# 10_12_09 - STAT 409 Fall 2009 Examples for Hypotheses...

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STAT 409 Examples for 10/12/2009 Fall 2009 Hypotheses Testing for the population mean μ Null Alternative H 0 : μ μ 0 vs. H 1 : μ < μ 0 Left - tailed. H 0 : μ μ 0 vs. H 1 : μ > μ 0 Right - tailed. H 0 : μ = μ 0 vs. H 1 : μ μ 0 Two - tailed. Test Statistic: n σ μ 0 X Z - = OR n s 0 μ X T - = OR X Rejection Region: H 0 : μ μ 0 H 1 : μ < μ 0 Left - tailed. H 0 : μ μ 0 H 1 : μ > μ 0 Right - tailed. H 0 : μ = μ 0 H 1 : μ μ 0 Two - tailed. Reject H 0 if Z < – z α Reject H 0 if Z > z α Reject H 0 if Z < – z α / 2 or Z > z α / 2 Reject H 0 if x < μ 0 z α n σ Reject H 0 if x > μ 0 + z α n σ Reject H 0 if x < μ 0 z α / 2 n σ or x > μ 0 + z α / 2 n σ

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1. The overall standard deviation of the diameters of the ball bearings is σ = 0.005 mm. The overall mean diameter of the ball bearings must be 4.300 mm. A sample of 81 ball bearings had a sample mean diameter of 4.299 mm. Is there a reason to believe that the actual overall mean diameter of the ball bearings is not 4.300 mm? a)
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10_12_09 - STAT 409 Fall 2009 Examples for Hypotheses...

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